Abstract

Following research initiated by Tarski, Craig and Nemeti, and futher pursued by Sain and others, we show that for certain subsets G of $^\omega \omega $ , atomic countable G poiyadic algebras are completely representable. G polyadic algebras are obtained by restricting the similarity type and axiomatization of ω-dimensional polyadic algebras to finite quantifiers and substitutions in G. This contrasts the cases of cylindric and relation algebras